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library(ggplot2)
library(cluster)    # clustering algorithms
library(factoextra) # clustering visualization
Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library(dendextend) # for comparing two dendrograms

---------------------
Welcome to dendextend version 1.15.2
Type citation('dendextend') for how to cite the package.

Type browseVignettes(package = 'dendextend') for the package vignette.
The github page is: https://github.com/talgalili/dendextend/

Suggestions and bug-reports can be submitted at: https://github.com/talgalili/dendextend/issues
You may ask questions at stackoverflow, use the r and dendextend tags: 
     https://stackoverflow.com/questions/tagged/dendextend

    To suppress this message use:  suppressPackageStartupMessages(library(dendextend))
---------------------


Attaching package: ‘dendextend’

The following object is masked from ‘package:stats’:

    cutree
library(tidyr) # Load tidyr
library(sparcl) # Sparse Clustering
library(tidyverse)
Registered S3 methods overwritten by 'dbplyr':
  method         from
  print.tbl_lazy     
  print.tbl_sql      
── Attaching packages ───────────────────────────────────────── tidyverse 1.3.0 ──
✓ tibble  3.1.6     ✓ dplyr   1.0.4
✓ readr   1.4.0     ✓ stringr 1.4.0
✓ purrr   0.3.4     ✓ forcats 0.5.1
── Conflicts ──────────────────────────────────────────── tidyverse_conflicts() ──
x dplyr::filter() masks stats::filter()
x dplyr::lag()    masks stats::lag()
data <- read.csv("athlete_data.csv")
summary(data)
 Participant.ID    Age..Years.         Sex             Sport     
 Min.   :  1.00   Min.   :-1.00   Min.   :0.0000   Min.   :1.00  
 1st Qu.: 46.50   1st Qu.:13.00   1st Qu.:0.0000   1st Qu.:2.00  
 Median : 86.00   Median :14.00   Median :0.0000   Median :2.00  
 Mean   : 85.68   Mean   :14.33   Mean   :0.4903   Mean   :2.89  
 3rd Qu.:126.50   3rd Qu.:16.00   3rd Qu.:1.0000   3rd Qu.:5.00  
 Max.   :165.00   Max.   :18.00   Max.   :1.0000   Max.   :6.00  
 Concussion.History Concussion.Number Learning.Disability Anxiety.Diagnosis 
 Min.   :0.0000     Min.   :0.0000    Min.   :-1.00000    Min.   :-1.00000  
 1st Qu.:0.0000     1st Qu.:0.0000    1st Qu.: 0.00000    1st Qu.: 0.00000  
 Median :1.0000     Median :0.0000    Median : 0.00000    Median : 0.00000  
 Mean   :0.6839     Mean   :0.4258    Mean   : 0.08387    Mean   : 0.09677  
 3rd Qu.:1.0000     3rd Qu.:1.0000    3rd Qu.: 0.00000    3rd Qu.: 0.00000  
 Max.   :1.0000     Max.   :3.0000    Max.   : 1.00000    Max.   : 1.00000  
 Anxiety.Symptoms  Depression.Diagnosis X..of.Prior.Depressive.Episodes
 Min.   :-1.0000   Min.   :-1.00000     Min.   :-1.000                 
 1st Qu.: 1.0000   1st Qu.: 0.00000     1st Qu.: 0.000                 
 Median : 1.0000   Median : 0.00000     Median : 0.000                 
 Mean   : 0.7613   Mean   : 0.05806     Mean   : 0.471                 
 3rd Qu.: 1.0000   3rd Qu.: 0.00000     3rd Qu.: 0.000                 
 Max.   : 1.0000   Max.   : 1.00000     Max.   : 4.000                 
 Prior.Depressive.Episode.s..Y.N Aggregate.Medical.History
 Min.   :-1.0000                 Min.   :-1.0000          
 1st Qu.: 0.0000                 1st Qu.: 0.0000          
 Median : 0.0000                 Median : 0.0000          
 Mean   : 0.1677                 Mean   : 0.1613          
 3rd Qu.: 0.0000                 3rd Qu.: 0.0000          
 Max.   : 1.0000                 Max.   : 1.0000          
 PCS.Symptom.Frequency..22. PCS.Symptom.Severity..132.     MFQ.66      
 Min.   : 0.000             Min.   :  0.00             Min.   : 0.000  
 1st Qu.: 0.000             1st Qu.:  0.00             1st Qu.: 1.000  
 Median : 2.000             Median :  3.00             Median : 3.000  
 Mean   : 4.219             Mean   : 10.14             Mean   : 7.787  
 3rd Qu.: 6.000             3rd Qu.: 11.00             3rd Qu.: 9.000  
 Max.   :22.000             Max.   :104.00             Max.   :53.000  
  MFQ.Cut.off          PCS.1            PCS.2            PCS.3        
 Min.   :0.00000   Min.   :0.0000   Min.   :0.0000   Min.   :0.00000  
 1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000  
 Median :0.00000   Median :0.0000   Median :0.0000   Median :0.00000  
 Mean   :0.08387   Mean   :0.6129   Mean   :0.1935   Mean   :0.08387  
 3rd Qu.:0.00000   3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:0.00000  
 Max.   :1.00000   Max.   :6.0000   Max.   :5.0000   Max.   :5.00000  
     PCS.4            PCS.5            PCS.6            PCS.7    
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0  
 Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0  
 Mean   :0.2645   Mean   :0.3419   Mean   :0.9806   Mean   :0.8  
 3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:2.0000   3rd Qu.:1.0  
 Max.   :5.0000   Max.   :6.0000   Max.   :6.0000   Max.   :6.0  
     PCS.8            PCS.9            PCS.10           PCS.11      
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
 Mean   :0.5806   Mean   :0.5548   Mean   :0.4258   Mean   :0.2581  
 3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000  
 Max.   :6.0000   Max.   :6.0000   Max.   :5.0000   Max.   :6.0000  
     PCS12            PCS.13           PCS.14           PCS.15      
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
 Mean   :0.2258   Mean   :0.4774   Mean   :0.5419   Mean   :0.7419  
 3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:1.0000  
 Max.   :6.0000   Max.   :6.0000   Max.   :6.0000   Max.   :5.0000  
     PCS.16           PCS.17           PCS.18          PCS.19      
 Min.   :0.0000   Min.   :0.0000   Min.   :0.000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.000   1st Qu.:0.0000  
 Median :0.0000   Median :0.0000   Median :0.000   Median :0.0000  
 Mean   :0.4839   Mean   :0.2581   Mean   :0.329   Mean   :0.4129  
 3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.000   3rd Qu.:0.0000  
 Max.   :6.0000   Max.   :6.0000   Max.   :6.000   Max.   :6.0000  
     PCS.20           PCS.21           PCS.22           MFQ.1       
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
 Mean   :0.6903   Mean   :0.6065   Mean   :0.2774   Mean   :0.4065  
 3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:1.0000  
 Max.   :6.0000   Max.   :6.0000   Max.   :5.0000   Max.   :2.0000  
     MFQ.2            MFQ.3           MFQ.4            MFQ.5       
 Min.   :0.0000   Min.   :0.000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.0000   Median :0.000   Median :0.0000   Median :0.0000  
 Mean   :0.1419   Mean   :0.271   Mean   :0.2903   Mean   :0.5677  
 3rd Qu.:0.0000   3rd Qu.:0.000   3rd Qu.:0.0000   3rd Qu.:1.0000  
 Max.   :2.0000   Max.   :2.000   Max.   :2.0000   Max.   :2.0000  
     MFQ.6            MFQ.7            MFQ.8             MFQ9       
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
 Mean   :0.1677   Mean   :0.2387   Mean   :0.1871   Mean   :0.2903  
 3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000  
 Max.   :2.0000   Max.   :2.0000   Max.   :2.0000   Max.   :2.0000  
     MFQ.10           MFQ11            MFQ.12           MFQ.13       
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.00000  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000  
 Median :0.0000   Median :0.0000   Median :0.0000   Median :0.00000  
 Mean   :0.5032   Mean   :0.4258   Mean   :0.3097   Mean   :0.09677  
 3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.5000   3rd Qu.:0.00000  
 Max.   :2.0000   Max.   :2.0000   Max.   :2.0000   Max.   :2.00000  
     MFQ.14           MFQ.15           MFQ.16            MFQ.17      
 Min.   :0.0000   Min.   :0.0000   Min.   :0.00000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000  
 Median :0.0000   Median :0.0000   Median :0.00000   Median :0.0000  
 Mean   :0.1677   Mean   :0.1419   Mean   :0.09032   Mean   :0.1161  
 3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.00000   3rd Qu.:0.0000  
 Max.   :2.0000   Max.   :2.0000   Max.   :2.00000   Max.   :2.0000  
     MFQ.18            MFQ.19            MFQ.20           MFQ.21      
 Min.   :0.00000   Min.   :0.00000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.00000   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.00000   Median :0.00000   Median :0.0000   Median :0.0000  
 Mean   :0.09032   Mean   :0.06452   Mean   :0.1806   Mean   :0.3806  
 3rd Qu.:0.00000   3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:1.0000  
 Max.   :2.00000   Max.   :2.00000   Max.   :2.0000   Max.   :2.0000  
     MFQ.22           MFQ.23           MFQ.24           MFQ.25      
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
 Mean   :0.1806   Mean   :0.1548   Mean   :0.1935   Mean   :0.2581  
 3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000  
 Max.   :2.0000   Max.   :2.0000   Max.   :2.0000   Max.   :2.0000  
     MFQ.26          MFQ.27           MFQ.28           MFQ.29      
 Min.   :0.000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.000   Median :0.0000   Median :0.0000   Median :0.0000  
 Mean   :0.329   Mean   :0.2323   Mean   :0.1226   Mean   :0.3097  
 3rd Qu.:1.000   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000  
 Max.   :2.000   Max.   :2.0000   Max.   :2.0000   Max.   :2.0000  
     MFQ.30           MFQ.31           MFQ.32           MFQ.33      
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
 Mean   :0.2065   Mean   :0.1484   Mean   :0.2839   Mean   :0.2387  
 3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000  
 Max.   :2.0000   Max.   :2.0000   Max.   :2.0000   Max.   :2.0000  
head(data)
tail(data)
dim(data)
[1] 155  72
names(data)
 [1] "Participant.ID"                  "Age..Years."                    
 [3] "Sex"                             "Sport"                          
 [5] "Concussion.History"              "Concussion.Number"              
 [7] "Learning.Disability"             "Anxiety.Diagnosis"              
 [9] "Anxiety.Symptoms"                "Depression.Diagnosis"           
[11] "X..of.Prior.Depressive.Episodes" "Prior.Depressive.Episode.s..Y.N"
[13] "Aggregate.Medical.History"       "PCS.Symptom.Frequency..22."     
[15] "PCS.Symptom.Severity..132."      "MFQ.66"                         
[17] "MFQ.Cut.off"                     "PCS.1"                          
[19] "PCS.2"                           "PCS.3"                          
[21] "PCS.4"                           "PCS.5"                          
[23] "PCS.6"                           "PCS.7"                          
[25] "PCS.8"                           "PCS.9"                          
[27] "PCS.10"                          "PCS.11"                         
[29] "PCS12"                           "PCS.13"                         
[31] "PCS.14"                          "PCS.15"                         
[33] "PCS.16"                          "PCS.17"                         
[35] "PCS.18"                          "PCS.19"                         
[37] "PCS.20"                          "PCS.21"                         
[39] "PCS.22"                          "MFQ.1"                          
[41] "MFQ.2"                           "MFQ.3"                          
[43] "MFQ.4"                           "MFQ.5"                          
[45] "MFQ.6"                           "MFQ.7"                          
[47] "MFQ.8"                           "MFQ9"                           
[49] "MFQ.10"                          "MFQ11"                          
[51] "MFQ.12"                          "MFQ.13"                         
[53] "MFQ.14"                          "MFQ.15"                         
[55] "MFQ.16"                          "MFQ.17"                         
[57] "MFQ.18"                          "MFQ.19"                         
[59] "MFQ.20"                          "MFQ.21"                         
[61] "MFQ.22"                          "MFQ.23"                         
[63] "MFQ.24"                          "MFQ.25"                         
[65] "MFQ.26"                          "MFQ.27"                         
[67] "MFQ.28"                          "MFQ.29"                         
[69] "MFQ.30"                          "MFQ.31"                         
[71] "MFQ.32"                          "MFQ.33"                         
sapply(data, class)
                 Participant.ID                     Age..Years. 
                      "integer"                       "integer" 
                            Sex                           Sport 
                      "integer"                       "integer" 
             Concussion.History               Concussion.Number 
                      "integer"                       "integer" 
            Learning.Disability               Anxiety.Diagnosis 
                      "integer"                       "integer" 
               Anxiety.Symptoms            Depression.Diagnosis 
                      "integer"                       "integer" 
X..of.Prior.Depressive.Episodes Prior.Depressive.Episode.s..Y.N 
                      "integer"                       "integer" 
      Aggregate.Medical.History      PCS.Symptom.Frequency..22. 
                      "integer"                       "integer" 
     PCS.Symptom.Severity..132.                          MFQ.66 
                      "integer"                       "integer" 
                    MFQ.Cut.off                           PCS.1 
                      "integer"                       "integer" 
                          PCS.2                           PCS.3 
                      "integer"                       "integer" 
                          PCS.4                           PCS.5 
                      "integer"                       "integer" 
                          PCS.6                           PCS.7 
                      "integer"                       "integer" 
                          PCS.8                           PCS.9 
                      "integer"                       "integer" 
                         PCS.10                          PCS.11 
                      "integer"                       "integer" 
                          PCS12                          PCS.13 
                      "integer"                       "integer" 
                         PCS.14                          PCS.15 
                      "integer"                       "integer" 
                         PCS.16                          PCS.17 
                      "integer"                       "integer" 
                         PCS.18                          PCS.19 
                      "integer"                       "integer" 
                         PCS.20                          PCS.21 
                      "integer"                       "integer" 
                         PCS.22                           MFQ.1 
                      "integer"                       "integer" 
                          MFQ.2                           MFQ.3 
                      "integer"                       "integer" 
                          MFQ.4                           MFQ.5 
                      "integer"                       "integer" 
                          MFQ.6                           MFQ.7 
                      "integer"                       "integer" 
                          MFQ.8                            MFQ9 
                      "integer"                       "integer" 
                         MFQ.10                           MFQ11 
                      "integer"                       "integer" 
                         MFQ.12                          MFQ.13 
                      "integer"                       "integer" 
                         MFQ.14                          MFQ.15 
                      "integer"                       "integer" 
                         MFQ.16                          MFQ.17 
                      "integer"                       "integer" 
                         MFQ.18                          MFQ.19 
                      "integer"                       "integer" 
                         MFQ.20                          MFQ.21 
                      "integer"                       "integer" 
                         MFQ.22                          MFQ.23 
                      "integer"                       "integer" 
                         MFQ.24                          MFQ.25 
                      "integer"                       "integer" 
                         MFQ.26                          MFQ.27 
                      "integer"                       "integer" 
                         MFQ.28                          MFQ.29 
                      "integer"                       "integer" 
                         MFQ.30                          MFQ.31 
                      "integer"                       "integer" 
                         MFQ.32                          MFQ.33 
                      "integer"                       "integer" 
summary(as.factor(data$Concussion.History))
  0   1 
 49 106 
#convert -1s into null values and then impute them
sum(data == -1) 
[1] 12
data [data == -1] <- NA
data <- data[ -c(73) ]
head(data)
sum(is.na(data))
[1] 12
#find columns with null values
colnames(data)[colSums(is.na(data)) > 0]
[1] "Age..Years."                     "Learning.Disability"            
[3] "Anxiety.Diagnosis"               "Anxiety.Symptoms"               
[5] "Depression.Diagnosis"            "X..of.Prior.Depressive.Episodes"
[7] "Prior.Depressive.Episode.s..Y.N" "Aggregate.Medical.History"      
#imputation
data$Age..Years.[is.na(data$Age..Years.)]<-mean(data$Age..Years.,na.rm=TRUE)
data$Learning.Disability[is.na(data$Learning.Disability)]<-mean(data$Learning.Disability,na.rm=TRUE)
data$Anxiety.Diagnosis[is.na(data$Anxiety.Diagnosis)]<-mean(data$Anxiety.Diagnosis,na.rm=TRUE)
data$Anxiety.Symptoms[is.na(data$Anxiety.Symptoms)]<-mean(data$Anxiety.Symptoms,na.rm=TRUE)
data$Depression.Diagnosis[is.na(data$Depression.Diagnosis)]<-mean(data$Depression.Diagnosis,na.rm=TRUE)
data$X..of.Prior.Depressive.Episodes[is.na(data$X..of.Prior.Depressive.Episodes)]<-mean(data$X..of.Prior.Depressive.Episodes,na.rm=TRUE)
data$Prior.Depressive.Episode.s..Y.N[is.na(data$Prior.Depressive.Episode.s..Y.N)]<-mean(data$Prior.Depressive.Episode.s..Y.N,na.rm=TRUE)
data$Aggregate.Medical.History[is.na(data$Aggregate.Medical.History)]<-mean(data$Aggregate.Medical.History,na.rm=TRUE)

sum(is.na(data))
[1] 0
plot_dat <- data
plot_dat$Concussion.History <- as.factor(plot_dat$Concussion.History) 
g_1 <- ggplot(plot_dat, aes(x = PCS.Symptom.Severity..132., fill = Concussion.History)) +
  geom_density(alpha = 0.5) +
    theme_set(theme_bw(base_size = 11) ) + 
  theme(panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), 
        panel.border = element_blank(), 
        panel.background = element_blank()) + 
  labs(x = "Symptom Severity", title = "Relationship Between Symptom Severity and Concussion History", fill = "Diagnosis") + # Set labels
  scale_fill_manual(values = c("1" = "red", "0" = "blue"), 
                    labels = c("1" = "Concussion History", "0" = "No Concussion History"))
g_1

plot_dat <- data
plot_dat$Depression.Diagnosis <- as.factor(plot_dat$Depression.Diagnosis) 
g_2 <- ggplot(plot_dat, aes(x = PCS.Symptom.Severity..132., fill = Depression.Diagnosis)) +
  geom_density(alpha = 0.5) +
    theme_set(theme_bw(base_size = 11) ) + 
  theme(panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), 
        panel.border = element_blank(), 
        panel.background = element_blank()) + 
  labs(x = "Symptom Severity", title = "Relationship Between Symptom Severity and Depression Diagnosis", fill = "Diagnosis") + # Set labels
  scale_fill_manual(values = c("1" = "red", "0" = "blue"), 
                    labels = c("1" = "Depression Diagnosis", "0" = "No Diagnosis"))
g_2

plot_dat <- data
plot_dat$Depression.Diagnosis <- as.factor(plot_dat$Depression.Diagnosis) 
g_4 <- ggplot(plot_dat, aes(x = factor(Concussion.History), fill = Depression.Diagnosis)) +
  geom_bar(alpha = 0.5, position = "dodge") +
    theme_set(theme_bw(base_size = 11) ) + 
  theme(panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), 
        panel.border = element_blank(), 
        panel.background = element_blank()) + 
  labs(x = "Concussion History", title = "Relationship Between Concussion History and Depression Diagnosis", fill = "Diagnosis") + # Set labels
  scale_fill_manual(values = c("1" = "red", "0" = "blue"), 
                    labels = c("1" = "Depression Diagnosis", "0" = "No Diagnosis"))
g_4

plot_dat <- data
plot_dat$Anxiety.Diagnosis <- as.factor(plot_dat$Anxiety.Diagnosis) 
g_3 <- ggplot(plot_dat, aes(x = PCS.Symptom.Severity..132., fill = Anxiety.Diagnosis)) +
  geom_density(alpha = 0.5) +
    theme_set(theme_bw(base_size = 11) ) + 
  theme(panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), 
        panel.border = element_blank(), 
        panel.background = element_blank()) + 
  labs(x = "Symptom Severity", title = "Relationship Between Symptom Severity and Anxiety Diagnosis", fill = "Diagnosis") + # Set labels
  scale_fill_manual(values = c("1" = "red", "0" = "blue"), 
                    labels = c("1" = "Anxiety Diagnosis", "0" = "No Diagnosis"))
g_3

Hierarchical Clustering

sdata <- scale(data[,-1])
summary(sdata)
  Age..Years.          Sex              Sport         Concussion.History
 Min.   :-1.216   Min.   :-0.9777   Min.   :-1.1298   Min.   :-1.4661   
 1st Qu.:-1.216   1st Qu.:-0.9777   1st Qu.:-0.5321   1st Qu.:-1.4661   
 Median : 0.000   Median :-0.9777   Median :-0.5321   Median : 0.6777   
 Mean   : 0.000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   
 3rd Qu.: 1.020   3rd Qu.: 1.0163   3rd Qu.: 1.2609   3rd Qu.: 0.6777   
 Max.   : 2.510   Max.   : 1.0163   Max.   : 1.8585   Max.   : 0.6777   
 Concussion.Number Learning.Disability Anxiety.Diagnosis Anxiety.Symptoms 
 Min.   :-0.5912   Min.   :-0.3162     Min.   :-0.3405   Min.   :-1.9886  
 1st Qu.:-0.5912   1st Qu.:-0.3162     1st Qu.:-0.3405   1st Qu.: 0.5095  
 Median :-0.5912   Median :-0.3162     Median :-0.3405   Median : 0.5095  
 Mean   : 0.0000   Mean   : 0.0000     Mean   : 0.0000   Mean   : 0.0000  
 3rd Qu.: 0.7972   3rd Qu.:-0.3162     3rd Qu.:-0.3405   3rd Qu.: 0.5095  
 Max.   : 3.5739   Max.   : 3.1623     Max.   : 2.9368   Max.   : 0.5095  
 Depression.Diagnosis X..of.Prior.Depressive.Episodes
 Min.   :-0.2635      Min.   :-0.4111                
 1st Qu.:-0.2635      1st Qu.:-0.4111                
 Median :-0.2635      Median :-0.4111                
 Mean   : 0.0000      Mean   : 0.0000                
 3rd Qu.:-0.2635      3rd Qu.:-0.4111                
 Max.   : 3.7947      Max.   : 3.0107                
 Prior.Depressive.Episode.s..Y.N Aggregate.Medical.History
 Min.   :-0.4611                 Min.   :-0.4507          
 1st Qu.:-0.4611                 1st Qu.:-0.4507          
 Median :-0.4611                 Median :-0.4507          
 Mean   : 0.0000                 Mean   : 0.0000          
 3rd Qu.:-0.4611                 3rd Qu.:-0.4507          
 Max.   : 2.1688                 Max.   : 2.2188          
 PCS.Symptom.Frequency..22. PCS.Symptom.Severity..132.     MFQ.66       
 Min.   :-0.827             Min.   :-0.57098           Min.   :-0.6845  
 1st Qu.:-0.827             1st Qu.:-0.57098           1st Qu.:-0.5966  
 Median :-0.435             Median :-0.40208           Median :-0.4208  
 Mean   : 0.000             Mean   : 0.00000           Mean   : 0.0000  
 3rd Qu.: 0.349             3rd Qu.: 0.04831           3rd Qu.: 0.1066  
 Max.   : 3.485             Max.   : 5.28412           Max.   : 3.9746  
  MFQ.Cut.off          PCS.1             PCS.2             PCS.3        
 Min.   :-0.3016   Min.   :-0.5051   Min.   :-0.2587   Min.   :-0.1504  
 1st Qu.:-0.3016   1st Qu.:-0.5051   1st Qu.:-0.2587   1st Qu.:-0.1504  
 Median :-0.3016   Median :-0.5051   Median :-0.2587   Median :-0.1504  
 Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
 3rd Qu.:-0.3016   3rd Qu.: 0.3190   3rd Qu.:-0.2587   3rd Qu.:-0.1504  
 Max.   : 3.2943   Max.   : 4.4393   Max.   : 6.4246   Max.   : 8.8140  
     PCS.4             PCS.5             PCS.6             PCS.7       
 Min.   :-0.3313   Min.   :-0.3654   Min.   :-0.6610   Min.   :-0.556  
 1st Qu.:-0.3313   1st Qu.:-0.3654   1st Qu.:-0.6610   1st Qu.:-0.556  
 Median :-0.3313   Median :-0.3654   Median :-0.6610   Median :-0.556  
 Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.000  
 3rd Qu.:-0.3313   3rd Qu.:-0.3654   3rd Qu.: 0.6871   3rd Qu.: 0.139  
 Max.   : 5.9316   Max.   : 6.0459   Max.   : 3.3833   Max.   : 3.614  
     PCS.8             PCS.9             PCS.10            PCS.11       
 Min.   :-0.4263   Min.   :-0.4423   Min.   :-0.4153   Min.   :-0.2653  
 1st Qu.:-0.4263   1st Qu.:-0.4423   1st Qu.:-0.4153   1st Qu.:-0.2653  
 Median :-0.4263   Median :-0.4423   Median :-0.4153   Median :-0.2653  
 Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
 3rd Qu.:-0.4263   3rd Qu.:-0.4423   3rd Qu.:-0.4153   3rd Qu.:-0.2653  
 Max.   : 3.9785   Max.   : 4.3412   Max.   : 4.4612   Max.   : 5.9037  
     PCS12            PCS.13            PCS.14            PCS.15       
 Min.   :-0.276   Min.   :-0.4291   Min.   :-0.4059   Min.   :-0.6102  
 1st Qu.:-0.276   1st Qu.:-0.4291   1st Qu.:-0.4059   1st Qu.:-0.6102  
 Median :-0.276   Median :-0.4291   Median :-0.4059   Median :-0.6102  
 Mean   : 0.000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
 3rd Qu.:-0.276   3rd Qu.:-0.4291   3rd Qu.:-0.4059   3rd Qu.: 0.2122  
 Max.   : 7.057   Max.   : 4.9632   Max.   : 4.0883   Max.   : 3.5020  
     PCS.16            PCS.17            PCS.18            PCS.19       
 Min.   :-0.3886   Min.   :-0.2812   Min.   :-0.3167   Min.   :-0.3458  
 1st Qu.:-0.3886   1st Qu.:-0.2812   1st Qu.:-0.3167   1st Qu.:-0.3458  
 Median :-0.3886   Median :-0.2812   Median :-0.3167   Median :-0.3458  
 Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
 3rd Qu.:-0.3886   3rd Qu.:-0.2812   3rd Qu.:-0.3167   3rd Qu.:-0.3458  
 Max.   : 4.4306   Max.   : 6.2573   Max.   : 5.4585   Max.   : 4.6790  
     PCS.20            PCS.21            PCS.22           MFQ.1        
 Min.   :-0.4937   Min.   :-0.4555   Min.   :-0.303   Min.   :-0.7177  
 1st Qu.:-0.4937   1st Qu.:-0.4555   1st Qu.:-0.303   1st Qu.:-0.7177  
 Median :-0.4937   Median :-0.4555   Median :-0.303   Median :-0.7177  
 Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.000   Mean   : 0.0000  
 3rd Qu.: 0.2215   3rd Qu.:-0.4555   3rd Qu.:-0.303   3rd Qu.: 1.0480  
 Max.   : 3.7971   Max.   : 4.0510   Max.   : 5.159   Max.   : 2.8138  
     MFQ.2             MFQ.3             MFQ.4             MFQ.5        
 Min.   :-0.3683   Min.   :-0.4925   Min.   :-0.5204   Min.   :-0.7779  
 1st Qu.:-0.3683   1st Qu.:-0.4925   1st Qu.:-0.5204   1st Qu.:-0.7779  
 Median :-0.3683   Median :-0.4925   Median :-0.5204   Median :-0.7779  
 Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
 3rd Qu.:-0.3683   3rd Qu.:-0.4925   3rd Qu.:-0.5204   3rd Qu.: 0.5922  
 Max.   : 4.8208   Max.   : 3.1425   Max.   : 3.0644   Max.   : 1.9623  
     MFQ.6             MFQ.7             MFQ.8              MFQ9        
 Min.   :-0.3701   Min.   :-0.4268   Min.   :-0.3691   Min.   :-0.4817  
 1st Qu.:-0.3701   1st Qu.:-0.4268   1st Qu.:-0.3691   1st Qu.:-0.4817  
 Median :-0.3701   Median :-0.4268   Median :-0.3691   Median :-0.4817  
 Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
 3rd Qu.:-0.3701   3rd Qu.:-0.4268   3rd Qu.:-0.3691   3rd Qu.:-0.4817  
 Max.   : 4.0424   Max.   : 3.1493   Max.   : 3.5763   Max.   : 2.8368  
     MFQ.10            MFQ11             MFQ.12            MFQ.13       
 Min.   :-0.7322   Min.   :-0.6509   Min.   :-0.5374   Min.   :-0.2716  
 1st Qu.:-0.7322   1st Qu.:-0.6509   1st Qu.:-0.5374   1st Qu.:-0.2716  
 Median :-0.7322   Median :-0.6509   Median :-0.5374   Median :-0.2716  
 Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
 3rd Qu.: 0.7228   3rd Qu.: 0.8778   3rd Qu.: 0.3303   3rd Qu.:-0.2716  
 Max.   : 2.1777   Max.   : 2.4065   Max.   : 2.9334   Max.   : 5.3419  
     MFQ.14            MFQ.15            MFQ.16           MFQ.17       
 Min.   :-0.3487   Min.   :-0.3278   Min.   :-0.274   Min.   :-0.2947  
 1st Qu.:-0.3487   1st Qu.:-0.3278   1st Qu.:-0.274   1st Qu.:-0.2947  
 Median :-0.3487   Median :-0.3278   Median :-0.274   Median :-0.2947  
 Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.000   Mean   : 0.0000  
 3rd Qu.:-0.3487   3rd Qu.:-0.3278   3rd Qu.:-0.274   3rd Qu.:-0.2947  
 Max.   : 3.8088   Max.   : 4.2908   Max.   : 5.793   Max.   : 4.7811  
     MFQ.18           MFQ.19            MFQ.20           MFQ.21       
 Min.   :-0.274   Min.   :-0.2191   Min.   :-0.403   Min.   :-0.6071  
 1st Qu.:-0.274   1st Qu.:-0.2191   1st Qu.:-0.403   1st Qu.:-0.6071  
 Median :-0.274   Median :-0.2191   Median :-0.403   Median :-0.6071  
 Mean   : 0.000   Mean   : 0.0000   Mean   : 0.000   Mean   : 0.0000  
 3rd Qu.:-0.274   3rd Qu.:-0.2191   3rd Qu.:-0.403   3rd Qu.: 0.9878  
 Max.   : 5.793   Max.   : 6.5725   Max.   : 4.059   Max.   : 2.5827  
     MFQ.22           MFQ.23           MFQ.24            MFQ.25       
 Min.   :-0.403   Min.   :-0.319   Min.   :-0.3886   Min.   :-0.4738  
 1st Qu.:-0.403   1st Qu.:-0.319   1st Qu.:-0.3886   1st Qu.:-0.4738  
 Median :-0.403   Median :-0.319   Median :-0.3886   Median :-0.4738  
 Mean   : 0.000   Mean   : 0.000   Mean   : 0.0000   Mean   : 0.0000  
 3rd Qu.:-0.403   3rd Qu.:-0.319   3rd Qu.:-0.3886   3rd Qu.:-0.4738  
 Max.   : 4.059   Max.   : 3.801   Max.   : 3.6274   Max.   : 3.1985  
     MFQ.26            MFQ.27            MFQ.28            MFQ.29       
 Min.   :-0.5762   Min.   :-0.3935   Min.   :-0.2747   Min.   :-0.4915  
 1st Qu.:-0.5762   1st Qu.:-0.3935   1st Qu.:-0.2747   1st Qu.:-0.4915  
 Median :-0.5762   Median :-0.3935   Median :-0.2747   Median :-0.4915  
 Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
 3rd Qu.: 1.1750   3rd Qu.:-0.3935   3rd Qu.:-0.2747   3rd Qu.:-0.4915  
 Max.   : 2.9261   Max.   : 2.9953   Max.   : 4.2069   Max.   : 2.6828  
     MFQ.30            MFQ.31            MFQ.32            MFQ.33       
 Min.   :-0.3889   Min.   :-0.3385   Min.   :-0.4816   Min.   :-0.4268  
 1st Qu.:-0.3889   1st Qu.:-0.3385   1st Qu.:-0.4816   1st Qu.:-0.4268  
 Median :-0.3889   Median :-0.3385   Median :-0.4816   Median :-0.4268  
 Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000   Mean   : 0.0000  
 3rd Qu.:-0.3889   3rd Qu.:-0.3385   3rd Qu.:-0.4816   3rd Qu.:-0.4268  
 Max.   : 3.3788   Max.   : 4.2243   Max.   : 2.9113   Max.   : 3.1493  
# Calculate distances between points
dist_mat <- dist(sdata, # Set dataset
                 method = "euclidean") # Set distance measure to use
# Run hierarchical clustering
hc <- hclust(dist_mat, # Set distance matrix to use 
              method = "average" ) # Set linkage measure to use, for all the points in the cluster, what is the avg distance
plot(hc, # Set hierarchical clustering as plot object
     cex = 0.6, # Set text size
     hang = -1 ) # Set label position

# Create dendrogram
dend <- as.dendrogram(hc)
# order it the closest we can to the order of the observations:
dend <- rotate(dend, 1:50)
number of items to replace is not a multiple of replacement length
# Color the branches based on the clusters:
dend <- color_branches(dend, k=10) 

# We hang the dendrogram a bit:
dend <- hang.dendrogram(dend,hang_height=0.1)
# reduce the size of the labels:
dend <- set(dend, "labels_cex", 0.55)
# And plot:
par(mar = c(3,3,3,7))
plot(dend, 
     main = "Clustered Concussion Data",
     horiz =  TRUE,  nodePar = list(cex = .007))

clusters <- cutree(hc, # Specify object
                   k = 5) # Specify number of clusters
#look @ every cluster and find avg of variables
clustermeans <- as.data.frame(matrix(NA, nrow = 5, ncol = ncol(sdata)))
for(i in 1:5){
  if (sum(clusters == i) > 1){
    clustermeans[i, ] <- colMeans(sdata[clusters == i,])
  }
  else{
    clustermeans[i,] <- sdata[clusters == i,]
  }
  
}
names(clustermeans) <- names(data)[-1]
clustermeans
summary(as.factor(clusters))
  1   2   3   4   5 
146   5   2   1   1 
fviz_cluster(list(data = data, # Set data
                  cluster = clusters)) # Set clusters

cbind(row.names(data), clusters)
             clusters
  [1,] "1"   "1"     
  [2,] "2"   "1"     
  [3,] "3"   "1"     
  [4,] "4"   "1"     
  [5,] "5"   "1"     
  [6,] "6"   "1"     
  [7,] "7"   "1"     
  [8,] "8"   "1"     
  [9,] "9"   "1"     
 [10,] "10"  "1"     
 [11,] "11"  "1"     
 [12,] "12"  "2"     
 [13,] "13"  "1"     
 [14,] "14"  "2"     
 [15,] "15"  "1"     
 [16,] "16"  "1"     
 [17,] "17"  "1"     
 [18,] "18"  "1"     
 [19,] "19"  "1"     
 [20,] "20"  "1"     
 [21,] "21"  "1"     
 [22,] "22"  "1"     
 [23,] "23"  "1"     
 [24,] "24"  "1"     
 [25,] "25"  "1"     
 [26,] "26"  "1"     
 [27,] "27"  "1"     
 [28,] "28"  "1"     
 [29,] "29"  "1"     
 [30,] "30"  "1"     
 [31,] "31"  "1"     
 [32,] "32"  "1"     
 [33,] "33"  "1"     
 [34,] "34"  "1"     
 [35,] "35"  "1"     
 [36,] "36"  "1"     
 [37,] "37"  "1"     
 [38,] "38"  "1"     
 [39,] "39"  "1"     
 [40,] "40"  "1"     
 [41,] "41"  "1"     
 [42,] "42"  "1"     
 [43,] "43"  "1"     
 [44,] "44"  "1"     
 [45,] "45"  "1"     
 [46,] "46"  "3"     
 [47,] "47"  "1"     
 [48,] "48"  "1"     
 [49,] "49"  "1"     
 [50,] "50"  "1"     
 [51,] "51"  "2"     
 [52,] "52"  "1"     
 [53,] "53"  "1"     
 [54,] "54"  "1"     
 [55,] "55"  "1"     
 [56,] "56"  "1"     
 [57,] "57"  "1"     
 [58,] "58"  "1"     
 [59,] "59"  "1"     
 [60,] "60"  "1"     
 [61,] "61"  "1"     
 [62,] "62"  "1"     
 [63,] "63"  "1"     
 [64,] "64"  "3"     
 [65,] "65"  "1"     
 [66,] "66"  "1"     
 [67,] "67"  "1"     
 [68,] "68"  "1"     
 [69,] "69"  "1"     
 [70,] "70"  "1"     
 [71,] "71"  "1"     
 [72,] "72"  "2"     
 [73,] "73"  "1"     
 [74,] "74"  "4"     
 [75,] "75"  "1"     
 [76,] "76"  "1"     
 [77,] "77"  "1"     
 [78,] "78"  "2"     
 [79,] "79"  "5"     
 [80,] "80"  "1"     
 [81,] "81"  "1"     
 [82,] "82"  "1"     
 [83,] "83"  "1"     
 [84,] "84"  "1"     
 [85,] "85"  "1"     
 [86,] "86"  "1"     
 [87,] "87"  "1"     
 [88,] "88"  "1"     
 [89,] "89"  "1"     
 [90,] "90"  "1"     
 [91,] "91"  "1"     
 [92,] "92"  "1"     
 [93,] "93"  "1"     
 [94,] "94"  "1"     
 [95,] "95"  "1"     
 [96,] "96"  "1"     
 [97,] "97"  "1"     
 [98,] "98"  "1"     
 [99,] "99"  "1"     
[100,] "100" "1"     
[101,] "101" "1"     
[102,] "102" "1"     
[103,] "103" "1"     
[104,] "104" "1"     
[105,] "105" "1"     
[106,] "106" "1"     
[107,] "107" "1"     
[108,] "108" "1"     
[109,] "109" "1"     
[110,] "110" "1"     
[111,] "111" "1"     
[112,] "112" "1"     
[113,] "113" "1"     
[114,] "114" "1"     
[115,] "115" "1"     
[116,] "116" "1"     
[117,] "117" "1"     
[118,] "118" "1"     
[119,] "119" "1"     
[120,] "120" "1"     
[121,] "121" "1"     
[122,] "122" "1"     
[123,] "123" "1"     
[124,] "124" "1"     
[125,] "125" "1"     
[126,] "126" "1"     
[127,] "127" "1"     
[128,] "128" "1"     
[129,] "129" "1"     
[130,] "130" "1"     
[131,] "131" "1"     
[132,] "132" "1"     
[133,] "133" "1"     
[134,] "134" "1"     
[135,] "135" "1"     
[136,] "136" "1"     
[137,] "137" "1"     
[138,] "138" "1"     
[139,] "139" "1"     
[140,] "140" "1"     
[141,] "141" "1"     
[142,] "142" "1"     
[143,] "143" "1"     
[144,] "144" "1"     
[145,] "145" "1"     
[146,] "146" "1"     
[147,] "147" "1"     
[148,] "148" "1"     
[149,] "149" "1"     
[150,] "150" "1"     
[151,] "151" "1"     
[152,] "152" "1"     
[153,] "153" "1"     
[154,] "154" "1"     
[155,] "155" "1"     
colMeans(data[clusters == 1,])
                 Participant.ID                     Age..Years. 
                   85.520547945                    14.618240807 
                            Sex                           Sport 
                    0.520547945                     2.801369863 
             Concussion.History               Concussion.Number 
                    0.684931507                     0.424657534 
            Learning.Disability               Anxiety.Diagnosis 
                    0.075965131                     0.089752713 
               Anxiety.Symptoms            Depression.Diagnosis 
                    0.824576424                     0.048389966 
X..of.Prior.Depressive.Episodes Prior.Depressive.Episode.s..Y.N 
                    0.366304928                     0.138187155 
      Aggregate.Medical.History      PCS.Symptom.Frequency..22. 
                    0.151841309                     3.390410959 
     PCS.Symptom.Severity..132.                          MFQ.66 
                    6.842465753                     5.609589041 
                    MFQ.Cut.off                           PCS.1 
                    0.027397260                     0.465753425 
                          PCS.2                           PCS.3 
                    0.123287671                     0.027397260 
                          PCS.4                           PCS.5 
                    0.150684932                     0.212328767 
                          PCS.6                           PCS.7 
                    0.787671233                     0.657534247 
                          PCS.8                           PCS.9 
                    0.431506849                     0.417808219 
                         PCS.10                          PCS.11 
                    0.273972603                     0.130136986 
                          PCS12                          PCS.13 
                    0.123287671                     0.321917808 
                         PCS.14                          PCS.15 
                    0.328767123                     0.595890411 
                         PCS.16                          PCS.17 
                    0.232876712                     0.123287671 
                         PCS.18                          PCS.19 
                    0.157534247                     0.205479452 
                         PCS.20                          PCS.21 
                    0.472602740                     0.452054795 
                         PCS.22                           MFQ.1 
                    0.150684932                     0.349315068 
                          MFQ.2                           MFQ.3 
                    0.095890411                     0.226027397 
                          MFQ.4                           MFQ.5 
                    0.253424658                     0.506849315 
                          MFQ.6                           MFQ.7 
                    0.102739726                     0.178082192 
                          MFQ.8                            MFQ9 
                    0.089041096                     0.198630137 
                         MFQ.10                           MFQ11 
                    0.431506849                     0.356164384 
                         MFQ.12                          MFQ.13 
                    0.253424658                     0.041095890 
                         MFQ.14                          MFQ.15 
                    0.095890411                     0.082191781 
                         MFQ.16                          MFQ.17 
                    0.027397260                     0.061643836 
                         MFQ.18                          MFQ.19 
                    0.027397260                     0.006849315 
                         MFQ.20                          MFQ.21 
                    0.136986301                     0.294520548 
                         MFQ.22                          MFQ.23 
                    0.123287671                     0.068493151 
                         MFQ.24                          MFQ.25 
                    0.136986301                     0.171232877 
                         MFQ.26                          MFQ.27 
                    0.273972603                     0.130136986 
                         MFQ.28                          MFQ.29 
                    0.041095890                     0.232876712 
                         MFQ.30                          MFQ.31 
                    0.123287671                     0.075342466 
                         MFQ.32                          MFQ.33 
                    0.219178082                     0.198630137 
colMeans(data[clusters == 2,])
                 Participant.ID                     Age..Years. 
                          102.4                            14.6 
                            Sex                           Sport 
                            0.0                             5.4 
             Concussion.History               Concussion.Number 
                            0.6                             0.6 
            Learning.Disability               Anxiety.Diagnosis 
                            0.4                             0.4 
               Anxiety.Symptoms            Depression.Diagnosis 
                            0.4                             0.2 
X..of.Prior.Depressive.Episodes Prior.Depressive.Episode.s..Y.N 
                            2.4                             0.8 
      Aggregate.Medical.History      PCS.Symptom.Frequency..22. 
                            0.4                            15.6 
     PCS.Symptom.Severity..132.                          MFQ.66 
                           43.4                            44.8 
                    MFQ.Cut.off                           PCS.1 
                            1.0                             1.8 
                          PCS.2                           PCS.3 
                            0.2                             0.0 
                          PCS.4                           PCS.5 
                            1.0                             1.0 
                          PCS.6                           PCS.7 
                            2.8                             1.6 
                          PCS.8                           PCS.9 
                            2.0                             2.4 
                         PCS.10                          PCS.11 
                            1.8                             0.8 
                          PCS12                          PCS.13 
                            0.6                             2.4 
                         PCS.14                          PCS.15 
                            3.8                             2.4 
                         PCS.16                          PCS.17 
                            4.6                             1.8 
                         PCS.18                          PCS.19 
                            2.4                             3.0 
                         PCS.20                          PCS.21 
                            3.6                             1.4 
                         PCS.22                           MFQ.1 
                            2.0                             1.8 
                          MFQ.2                           MFQ.3 
                            1.2                             1.2 
                          MFQ.4                           MFQ.5 
                            0.8                             1.4 
                          MFQ.6                           MFQ.7 
                            1.2                             1.0 
                          MFQ.8                            MFQ9 
                            2.0                             2.0 
                         MFQ.10                           MFQ11 
                            1.6                             1.8 
                         MFQ.12                          MFQ.13 
                            1.2                             0.8 
                         MFQ.14                          MFQ.15 
                            1.2                             1.0 
                         MFQ.16                          MFQ.17 
                            1.2                             1.2 
                         MFQ.18                          MFQ.19 
                            1.4                             1.2 
                         MFQ.20                          MFQ.21 
                            0.8                             1.6 
                         MFQ.22                          MFQ.23 
                            1.0                             1.6 
                         MFQ.24                          MFQ.25 
                            1.4                             1.8 
                         MFQ.26                          MFQ.27 
                            1.4                             2.0 
                         MFQ.28                          MFQ.29 
                            1.8                             1.8 
                         MFQ.30                          MFQ.31 
                            1.6                             1.2 
                         MFQ.32                          MFQ.33 
                            1.2                             0.4 
colMeans(data[clusters == 4,])
                 Participant.ID                     Age..Years. 
                       71.00000                        14.63158 
                            Sex                           Sport 
                        0.00000                         3.00000 
             Concussion.History               Concussion.Number 
                        0.00000                         1.00000 
            Learning.Disability               Anxiety.Diagnosis 
                        0.00000                         0.00000 
               Anxiety.Symptoms            Depression.Diagnosis 
                        0.00000                         1.00000 
X..of.Prior.Depressive.Episodes Prior.Depressive.Episode.s..Y.N 
                        1.00000                         1.00000 
      Aggregate.Medical.History      PCS.Symptom.Frequency..22. 
                        1.00000                        19.00000 
     PCS.Symptom.Severity..132.                          MFQ.66 
                       94.00000                        35.00000 
                    MFQ.Cut.off                           PCS.1 
                        1.00000                         6.00000 
                          PCS.2                           PCS.3 
                        3.00000                         2.00000 
                          PCS.4                           PCS.5 
                        2.00000                         6.00000 
                          PCS.6                           PCS.7 
                        6.00000                         4.00000 
                          PCS.8                           PCS.9 
                        5.00000                         0.00000 
                         PCS.10                          PCS.11 
                        5.00000                         4.00000 
                          PCS12                          PCS.13 
                        6.00000                         6.00000 
                         PCS.14                          PCS.15 
                        6.00000                         5.00000 
                         PCS.16                          PCS.17 
                        5.00000                         0.00000 
                         PCS.18                          PCS.19 
                        6.00000                         6.00000 
                         PCS.20                          PCS.21 
                        5.00000                         6.00000 
                         PCS.22                           MFQ.1 
                        0.00000                         1.00000 
                          MFQ.2                           MFQ.3 
                        0.00000                         0.00000 
                          MFQ.4                           MFQ.5 
                        2.00000                         2.00000 
                          MFQ.6                           MFQ.7 
                        0.00000                         1.00000 
                          MFQ.8                            MFQ9 
                        1.00000                         2.00000 
                         MFQ.10                           MFQ11 
                        2.00000                         1.00000 
                         MFQ.12                          MFQ.13 
                        0.00000                         0.00000 
                         MFQ.14                          MFQ.15 
                        2.00000                         2.00000 
                         MFQ.16                          MFQ.17 
                        2.00000                         2.00000 
                         MFQ.18                          MFQ.19 
                        0.00000                         2.00000 
                         MFQ.20                          MFQ.21 
                        0.00000                         2.00000 
                         MFQ.22                          MFQ.23 
                        0.00000                         1.00000 
                         MFQ.24                          MFQ.25 
                        0.00000                         2.00000 
                         MFQ.26                          MFQ.27 
                        0.00000                         2.00000 
                         MFQ.28                          MFQ.29 
                        0.00000                         0.00000 
                         MFQ.30                          MFQ.31 
                        2.00000                         2.00000 
                         MFQ.32                          MFQ.33 
                        0.00000                         2.00000 
colMeans(data[clusters == 5,])
                 Participant.ID                     Age..Years. 
                             77                              14 
                            Sex                           Sport 
                              0                               3 
             Concussion.History               Concussion.Number 
                              1                               0 
            Learning.Disability               Anxiety.Diagnosis 
                              1                               1 
               Anxiety.Symptoms            Depression.Diagnosis 
                              0                               1 
X..of.Prior.Depressive.Episodes Prior.Depressive.Episode.s..Y.N 
                              4                               1 
      Aggregate.Medical.History      PCS.Symptom.Frequency..22. 
                              1                              18 
     PCS.Symptom.Severity..132.                          MFQ.66 
                             72                              49 
                    MFQ.Cut.off                           PCS.1 
                              1                               2 
                          PCS.2                           PCS.3 
                              0                               0 
                          PCS.4                           PCS.5 
                              4                               1 
                          PCS.6                           PCS.7 
                              6                               4 
                          PCS.8                           PCS.9 
                              2                               6 
                         PCS.10                          PCS.11 
                              4                               6 
                          PCS12                          PCS.13 
                              0                               0 
                         PCS.14                          PCS.15 
                              1                               2 
                         PCS.16                          PCS.17 
                              4                               6 
                         PCS.18                          PCS.19 
                              3                               4 
                         PCS.20                          PCS.21 
                              6                               6 
                         PCS.22                           MFQ.1 
                              5                               1 
                          MFQ.2                           MFQ.3 
                              1                               0 
                          MFQ.4                           MFQ.5 
                              2                               2 
                          MFQ.6                           MFQ.7 
                              2                               2 
                          MFQ.8                            MFQ9 
                              2                               2 
                         MFQ.10                           MFQ11 
                              2                               2 
                         MFQ.12                          MFQ.13 
                              2                               2 
                         MFQ.14                          MFQ.15 
                              2                               1 
                         MFQ.16                          MFQ.17 
                              0                               0 
                         MFQ.18                          MFQ.19 
                              1                               0 
                         MFQ.20                          MFQ.21 
                              2                               2 
                         MFQ.22                          MFQ.23 
                              2                               2 
                         MFQ.24                          MFQ.25 
                              1                               1 
                         MFQ.26                          MFQ.27 
                              2                               2 
                         MFQ.28                          MFQ.29 
                              2                               2 
                         MFQ.30                          MFQ.31 
                              2                               1 
                         MFQ.32                          MFQ.33 
                              2                               0 
remove outliers
sdata <- sdata[-c(74, 79), ]
set.seed(12345) # Set seed for reproducibility
fit_1 <- kmeans(x = sdata, # Set data as explantory variables 
                centers = 5,  # Set number of clusters
                nstart = 25, # Set number of starts
                iter.max = 100 ) # Set maximum number of iterations to use
# Extract clusters
clusters_1 <- fit_1$cluster
# Extract centers
centers_1 <- fit_1$centers
# Check samples per cluster
summary(as.factor(clusters_1))
  1   2   3   4   5 
113   1   6  25   1 
# Create vector of clusters
cluster <- c(1: 5)
# Extract centers
center_df <- data.frame(cluster, centers_1)

# Reshape the data
center_reshape <- gather(center_df, features, values, Age..Years.:MFQ.Cut.off)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
# Generate plot
g_heat_1

#makes case for dropping clusters 2 and 3 bc their values are so distinct from all of the others
# Create vector of clusters
cluster <- c(1: 5)
# Extract centers
center_df <- data.frame(cluster, centers_1)

# Reshape the data
center_reshape <- gather(center_df, features, values, PCS.1:PCS.22)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
# Generate plot
g_heat_1
ggsave(g_heat_1, file = "PCSPlot.jpeg", width = 8, height = 12, dpi = 600)

#makes case for dropping clusters 2 and 3 bc their values are so distinct from all of the others
# Create vector of clusters
cluster <- c(1: 5)
# Extract centers
center_df <- data.frame(cluster, centers_1)

# Reshape the data
center_reshape <- gather(center_df, features, values, MFQ.1:MFQ.33)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
# Generate plot
g_heat_1
ggsave(g_heat_1, file = "PCSPlot.jpeg", width = 8, height = 12, dpi = 600)

data2 <- data[!clusters %in% c(2,3,5),]
sdata2 <- scale(data2[,-1])
#head(sdata2)
# Create silhouette plot summary
fviz_nbclust(sdata2, # Set dataset
             kmeans,# Set clustering method
             method = "silhouette") # Set evaluation method

set.seed(12345) # Set seed for reproducibility
fit_2 <- kmeans(x = sdata2, # Set data as explantory variables 
                centers = 2,  # Set number of clusters
                nstart = 25, # Set number of starts
                iter.max = 100 ) # Set maximum number of iterations to use
# Extract clusters
clusters_2 <- fit_2$cluster
# Extract centers
centers_2 <- fit_2$centers
# Check samples per cluster
summary(as.factor(clusters_2))
  1   2 
 20 127 
# Create vector of clusters
cluster <- c(1: 2)
# Extract centers
center_df <- data.frame(cluster, centers_2)

# Reshape the data
center_reshape <- gather(center_df, features, values, Age..Years.:MFQ.Cut.off)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
# Generate plot
g_heat_1

# Create vector of clusters
cluster <- c(1: 2)
# Extract centers
center_df <- data.frame(cluster, centers_2)

# Reshape the data
center_reshape <- gather(center_df, features, values, PCS.1:PCS.22)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
# Generate plot
g_heat_1

# Create vector of clusters
cluster <- c(1: 2)
# Extract centers
center_df <- data.frame(cluster, centers_2)

# Reshape the data
center_reshape <- gather(center_df, features, values, MFQ.1:MFQ.33)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
# Generate plot
g_heat_1

#want our clusters to be balanced if possible (bad if cluster w much lower value)
plot_clust_cardinality <- as.data.frame(clusters_2)

names(plot_clust_cardinality) <- c("k_2") # Set names

# Create bar plots
g_2 <- ggplot(plot_clust_cardinality, aes( x = factor(k_2))) + # Set x as cluster values
  geom_bar(stat = "count", fill = "steelblue") + # Use geom_bar with stat = "count" to count observations
    labs(x = "Cluster Number", y="Points in Cluster", # Set labels
         title = "Cluster Cardinality (k = 4)") +
  theme(panel.grid.major = element_blank(), # Turn of the background grid
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank()) 
g_2

k_4_mag <- cbind.data.frame(c(1:2), fit_2$withinss) # Extract within cluster sum of squares

names(k_4_mag) <- c("cluster", "withinss") # Fix names for plot data


# Create bar plot
g_4 <- ggplot(k_4_mag, aes(x = cluster, y = withinss)) + # Set x as cluster, y as withinss
  geom_bar(stat = "identity", fill = "steelblue") + # Use geom bar and stat = "identity" to plot values directly
   labs(x = "Cluster Number", y="Total Point to Centroid Distance", # Set labels
         title = "Cluster Magnitude (k = 4)") +
  theme(panel.grid.major = element_blank(), # Turn of the background grid
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank()) 

g_4

k_4_dat <- cbind.data.frame(table(clusters_2), k_4_mag[,2]) # Join magnitude and cardinality

names(k_4_dat) <- c("cluster", "cardinality", "magnitude") # Fix plot data names # card = how many samples there are and magnitude = how much error there is in each cluster

# Create scatter plot
g_6 <- ggplot(k_4_dat, aes(x = cardinality, y = magnitude, color = cluster)) + # Set aesthetics
  geom_point(alpha = 0.8, size  = 4) +  # Set geom point for scatter
 geom_smooth(aes(x = cardinality, y = magnitude), method = "lm",
              se = FALSE, inherit.aes = FALSE, alpha = 0.5) + # Set trend  line
  labs(x = "Cluster Cardinality", y="Total Point to Centroid Distance", # Set labels
         title = "Cluster Magnitude vs Cardinality \n(k = 2)") +
  theme(panel.grid.major = element_blank(), # Turn of the background grid
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank()) 

g_6

# Calculate distance between samples
dis = dist(sdata2)^2
# Set plotting parameters to view plot
op <- par(mfrow= c(1,1), oma= c(0,0, 3, 0),
          mgp= c(1.6,.8,0), mar= .1+c(4,2,2,2))
# Create silhouette for k=4
#how similar sample is to others in its cluster/how dissimilar it is to vals in otherclusters
#want values to be as high as possible, if negative val more similar to vals in other clusters
sil = silhouette (clusters_2 , # Set clustering
                  dis, # Set distance 
                  full = TRUE) # Generate silhouette for all samples
# Generate silhouette plot
plot(sil)

# Create silhouette plot summary
fviz_nbclust(sdata2[clusters_2 ==1,], # Set dataset
             kmeans,# Set clustering method
             method = "silhouette") # Set evaluation method

Smaller group of data from sillouhette plot


set.seed(12345) # Set seed for reproducibility
fit_3 <- kmeans(x = sdata2[clusters_2 == 1,], # Set data as explantory variables 
                centers = 2,  # Set number of clusters
                nstart = 25, # Set number of starts
                iter.max = 100 ) # Set maximum number of iterations to use
# Extract clusters
clusters_3 <- fit_3$cluster
# Extract centers
centers_3 <- fit_3$centers
# Checksamples per cluster
summary(as.factor(clusters_3))
 1  2 
19  1 


set.seed(12345) # Set seed for reproducibility
fit_4 <- kmeans(x = sdata3, # Set data as explantory variables 
                centers = 3,  # Set number of clusters
                nstart = 25, # Set number of starts
                iter.max = 100 ) # Set maximum number of iterations to use
# Extract clusters
clusters_4 <- fit_4$cluster
# Extract centers
centers_4 <- fit_4$centers
# Checksamples per cluster
summary(as.factor(clusters_4))
 1  2  3 
 2 14  3 

Bigger group of data from silhouette plot

sdata5 <- sdata2[clusters_2 ==2,]
# Create silhouette plot summary
fviz_nbclust(sdata5, # Set dataset
             kmeans,# Set clustering method
             method = "silhouette") # Set evaluation method

set.seed(12345) # Set seed for reproducibility
fit_5 <- kmeans(x = sdata2[clusters_2 == 2,], # Set data as explantory variables 
                centers = 4,  # Set number of clusters
                nstart = 25, # Set number of starts
                iter.max = 100 ) # Set maximum number of iterations to use
# Extract clusters
clusters_5 <- fit_5$cluster
# Extract centers
centers_5 <- fit_5$centers
# Checksamples per cluster
summary(as.factor(clusters_5))
 1  2  3  4 
 8 12 67 40 
# Create vector of clusters
cluster <- c(1: 4)
# Extract centers
center_df <- data.frame(cluster, centers_5)

# Reshape the data
center_reshape <- gather(center_df, features, values, Age..Years.:MFQ.Cut.off)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
# Generate plot
g_heat_1

# Create vector of clusters
cluster <- c(1: 4)
# Extract centers
center_df <- data.frame(cluster, centers_5)

# Reshape the data
center_reshape <- gather(center_df, features, values, PCS.1:PCS.22)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
# Generate plot
g_heat_1

# Create vector of clusters
cluster <- c(1: 4)
# Extract centers
center_df <- data.frame(cluster, centers_5)

# Reshape the data
center_reshape <- gather(center_df, features, values, MFQ.1:MFQ.33)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
Coordinate system already present. Adding new coordinate system, which will replace the existing one.
# Generate plot
g_heat_1

plot_clust_cardinality <- as.data.frame(clusters_5)

names(plot_clust_cardinality) <- c("k_4") # Set names

# Create bar plots
g_6 <- ggplot(plot_clust_cardinality, aes( x = factor(k_4))) + # Set x as cluster values
  geom_bar(stat = "count", fill = "steelblue") + # Use geom_bar with stat = "count" to count observations
    labs(x = "Cluster Number", y="Points in Cluster", # Set labels
         title = "Cluster Cardinality (k = 4)") +
  theme(panel.grid.major = element_blank(), # Turn of the background grid
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank()) 
g_6

k_5_mag <- cbind.data.frame(c(1:4), fit_5$withinss) # Extract within cluster sum of squares
There were 27 warnings (use warnings() to see them)
names(k_5_mag) <- c("cluster", "withinss") # Fix names for plot data


# Create bar plot
g_7 <- ggplot(k_5_mag, aes(x = cluster, y = withinss)) + # Set x as cluster, y as withinss
  geom_bar(stat = "identity", fill = "steelblue") + # Use geom bar and stat = "identity" to plot values directly
   labs(x = "Cluster Number", y="Total Point to Centroid Distance", # Set labels
         title = "Cluster Magnitude (k = 4)") +
  theme(panel.grid.major = element_blank(), # Turn of the background grid
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank()) 

g_7

k_5_dat <- cbind.data.frame(table(clusters_5), k_5_mag[,2]) # Join magnitude and cardinality

names(k_5_dat) <- c("cluster", "cardinality", "magnitude") # Fix plot data names # card = how many samples there are and magnitude = how much error there is in each cluster

# Create scatter plot
g_8 <- ggplot(k_5_dat, aes(x = cardinality, y = magnitude, color = cluster)) + # Set aesthetics
  geom_point(alpha = 0.8, size  = 4) +  # Set geom point for scatter
 geom_smooth(aes(x = cardinality, y = magnitude), method = "lm",
              se = FALSE, inherit.aes = FALSE, alpha = 0.5) + # Set trend  line
  labs(x = "Cluster Cardinality", y="Total Point to Centroid Distance", # Set labels
         title = "Cluster Magnitude vs Cardinality \n(k = 4)") +
  theme(panel.grid.major = element_blank(), # Turn of the background grid
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank()) 

g_8

---
title: "R Notebook"
output: html_notebook
---

This is an [R Markdown](http://rmarkdown.rstudio.com) Notebook. When you execute code within the notebook, the results appear beneath the code. 

Try executing this chunk by clicking the *Run* button within the chunk or by placing your cursor inside it and pressing *Cmd+Shift+Enter*. 

```{r}
library(ggplot2)
library(cluster)    # clustering algorithms
library(factoextra) # clustering visualization
library(dendextend) # for comparing two dendrograms
library(tidyr) # Load tidyr
library(sparcl) # Sparse Clustering
library(tidyverse)
```

```{r}
data <- read.csv("athlete_data.csv")
```

```{r}
summary(data)
```


```{r}
head(data)
tail(data)
dim(data)
```
```{r}
names(data)
```
```{r}
sapply(data, class)
```


```{r}
summary(as.factor(data$Concussion.History))
```


```{r}
#convert -1s into null values and then impute them
sum(data == -1) 
data [data == -1] <- NA
data <- data[ -c(73) ]
head(data)
sum(is.na(data))
```

```{r}
#find columns with null values
colnames(data)[colSums(is.na(data)) > 0]
```


```{r}
#imputation
data$Age..Years.[is.na(data$Age..Years.)]<-mean(data$Age..Years.,na.rm=TRUE)
data$Learning.Disability[is.na(data$Learning.Disability)]<-mean(data$Learning.Disability,na.rm=TRUE)
data$Anxiety.Diagnosis[is.na(data$Anxiety.Diagnosis)]<-mean(data$Anxiety.Diagnosis,na.rm=TRUE)
data$Anxiety.Symptoms[is.na(data$Anxiety.Symptoms)]<-mean(data$Anxiety.Symptoms,na.rm=TRUE)
data$Depression.Diagnosis[is.na(data$Depression.Diagnosis)]<-mean(data$Depression.Diagnosis,na.rm=TRUE)
data$X..of.Prior.Depressive.Episodes[is.na(data$X..of.Prior.Depressive.Episodes)]<-mean(data$X..of.Prior.Depressive.Episodes,na.rm=TRUE)
data$Prior.Depressive.Episode.s..Y.N[is.na(data$Prior.Depressive.Episode.s..Y.N)]<-mean(data$Prior.Depressive.Episode.s..Y.N,na.rm=TRUE)
data$Aggregate.Medical.History[is.na(data$Aggregate.Medical.History)]<-mean(data$Aggregate.Medical.History,na.rm=TRUE)

sum(is.na(data))
```


```{r}
plot_dat <- data
plot_dat$Concussion.History <- as.factor(plot_dat$Concussion.History) 
g_1 <- ggplot(plot_dat, aes(x = PCS.Symptom.Severity..132., fill = Concussion.History)) +
  geom_density(alpha = 0.5) +
    theme_set(theme_bw(base_size = 11) ) + 
  theme(panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), 
        panel.border = element_blank(), 
        panel.background = element_blank()) + 
  labs(x = "Symptom Severity", title = "Relationship Between Symptom Severity and Concussion History", fill = "Diagnosis") + # Set labels
  scale_fill_manual(values = c("1" = "red", "0" = "blue"), 
                    labels = c("1" = "Concussion History", "0" = "No Concussion History"))
g_1
```

```{r}
plot_dat <- data
plot_dat$Depression.Diagnosis <- as.factor(plot_dat$Depression.Diagnosis) 
g_2 <- ggplot(plot_dat, aes(x = PCS.Symptom.Severity..132., fill = Depression.Diagnosis)) +
  geom_density(alpha = 0.5) +
    theme_set(theme_bw(base_size = 11) ) + 
  theme(panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), 
        panel.border = element_blank(), 
        panel.background = element_blank()) + 
  labs(x = "Symptom Severity", title = "Relationship Between Symptom Severity and Depression Diagnosis", fill = "Diagnosis") + # Set labels
  scale_fill_manual(values = c("1" = "red", "0" = "blue"), 
                    labels = c("1" = "Depression Diagnosis", "0" = "No Diagnosis"))
g_2
```

```{r}
plot_dat <- data
plot_dat$Depression.Diagnosis <- as.factor(plot_dat$Depression.Diagnosis) 
g_4 <- ggplot(plot_dat, aes(x = factor(Concussion.History), fill = Depression.Diagnosis)) +
  geom_bar(alpha = 0.5, position = "dodge") +
    theme_set(theme_bw(base_size = 11) ) + 
  theme(panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), 
        panel.border = element_blank(), 
        panel.background = element_blank()) + 
  labs(x = "Concussion History", title = "Relationship Between Concussion History and Depression Diagnosis", fill = "Diagnosis") + # Set labels
  scale_fill_manual(values = c("1" = "red", "0" = "blue"), 
                    labels = c("1" = "Depression Diagnosis", "0" = "No Diagnosis"))
g_4
```


```{r}
plot_dat <- data
plot_dat$Anxiety.Diagnosis <- as.factor(plot_dat$Anxiety.Diagnosis) 
g_3 <- ggplot(plot_dat, aes(x = PCS.Symptom.Severity..132., fill = Anxiety.Diagnosis)) +
  geom_density(alpha = 0.5) +
    theme_set(theme_bw(base_size = 11) ) + 
  theme(panel.grid.major = element_blank(), 
        panel.grid.minor = element_blank(), 
        panel.border = element_blank(), 
        panel.background = element_blank()) + 
  labs(x = "Symptom Severity", title = "Relationship Between Symptom Severity and Anxiety Diagnosis", fill = "Diagnosis") + # Set labels
  scale_fill_manual(values = c("1" = "red", "0" = "blue"), 
                    labels = c("1" = "Anxiety Diagnosis", "0" = "No Diagnosis"))
g_3
```

Hierarchical Clustering
```{r}
sdata <- scale(data[,-1])
```

```{r}
summary(sdata)
```

```{r}
# Calculate distances between points
dist_mat <- dist(sdata, # Set dataset
                 method = "euclidean") # Set distance measure to use
```

```{r}
# Run hierarchical clustering
hc <- hclust(dist_mat, # Set distance matrix to use 
              method = "average" ) # Set linkage measure to use, for all the points in the cluster, what is the avg distance
```

```{r}
plot(hc, # Set hierarchical clustering as plot object
     cex = 0.6, # Set text size
     hang = -1 ) # Set label position
```

```{r}
# Create dendrogram
dend <- as.dendrogram(hc)
# order it the closest we can to the order of the observations:
dend <- rotate(dend, 1:50)

# Color the branches based on the clusters:
dend <- color_branches(dend, k=10) 

# We hang the dendrogram a bit:
dend <- hang.dendrogram(dend,hang_height=0.1)
# reduce the size of the labels:
dend <- set(dend, "labels_cex", 0.55)
# And plot:
par(mar = c(3,3,3,7))
plot(dend, 
     main = "Clustered Concussion Data",
     horiz =  TRUE,  nodePar = list(cex = .007))
```

```{r}
clusters <- cutree(hc, # Specify object
                   k = 5) # Specify number of clusters
```

```{r}
#look @ every cluster and find avg of variables
clustermeans <- as.data.frame(matrix(NA, nrow = 5, ncol = ncol(sdata)))
for(i in 1:5){
  if (sum(clusters == i) > 1){
    clustermeans[i, ] <- colMeans(sdata[clusters == i,])
  }
  else{
    clustermeans[i,] <- sdata[clusters == i,]
  }
  
}
names(clustermeans) <- names(data)[-1]
```

```{r}
clustermeans
summary(as.factor(clusters))
```


```{r}
fviz_cluster(list(data = data, # Set data
                  cluster = clusters)) # Set clusters
```
```{r}
cbind(row.names(data), clusters)
```
```{r}
colMeans(data[clusters == 1,])
```
```{r}
colMeans(data[clusters == 2,])
```

```{r}
colMeans(data[clusters == 4,])
```
```{r}
colMeans(data[clusters == 5,])
```

```{r}
remove outliers
sdata <- sdata[-c(74, 79), ]
```


```{r}
set.seed(12345) # Set seed for reproducibility
fit_1 <- kmeans(x = sdata, # Set data as explantory variables 
                centers = 5,  # Set number of clusters
                nstart = 25, # Set number of starts
                iter.max = 100 ) # Set maximum number of iterations to use
```

```{r}
# Extract clusters
clusters_1 <- fit_1$cluster
# Extract centers
centers_1 <- fit_1$centers
# Check samples per cluster
summary(as.factor(clusters_1))
```
```{r}
# Create vector of clusters
cluster <- c(1: 5)
# Extract centers
center_df <- data.frame(cluster, centers_1)

# Reshape the data
center_reshape <- gather(center_df, features, values, Age..Years.:MFQ.Cut.off)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
# Generate plot
g_heat_1
```

```{r}
#makes case for dropping clusters 2 and 3 bc their values are so distinct from all of the others
# Create vector of clusters
cluster <- c(1: 5)
# Extract centers
center_df <- data.frame(cluster, centers_1)

# Reshape the data
center_reshape <- gather(center_df, features, values, PCS.1:PCS.22)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
# Generate plot
g_heat_1
ggsave(g_heat_1, file = "PCSPlot.jpeg", width = 8, height = 12, dpi = 600)
```

```{r}
#makes case for dropping clusters 2 and 3 bc their values are so distinct from all of the others
# Create vector of clusters
cluster <- c(1: 5)
# Extract centers
center_df <- data.frame(cluster, centers_1)

# Reshape the data
center_reshape <- gather(center_df, features, values, MFQ.1:MFQ.33)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
# Generate plot
g_heat_1
ggsave(g_heat_1, file = "PCSPlot.jpeg", width = 8, height = 12, dpi = 600)
```


```{r}
data2 <- data[!clusters %in% c(2,3,5),]
```

```{r}
sdata2 <- scale(data2[,-1])
#head(sdata2)
```


```{r}
# Create silhouette plot summary
fviz_nbclust(sdata2, # Set dataset
             kmeans,# Set clustering method
             method = "silhouette") # Set evaluation method
```

```{r}
set.seed(12345) # Set seed for reproducibility
fit_2 <- kmeans(x = sdata2, # Set data as explantory variables 
                centers = 2,  # Set number of clusters
                nstart = 25, # Set number of starts
                iter.max = 100 ) # Set maximum number of iterations to use
```


```{r}
# Extract clusters
clusters_2 <- fit_2$cluster
# Extract centers
centers_2 <- fit_2$centers
# Check samples per cluster
summary(as.factor(clusters_2))
```

```{r}
# Create vector of clusters
cluster <- c(1: 2)
# Extract centers
center_df <- data.frame(cluster, centers_2)

# Reshape the data
center_reshape <- gather(center_df, features, values, Age..Years.:MFQ.Cut.off)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
# Generate plot
g_heat_1
```

```{r}
# Create vector of clusters
cluster <- c(1: 2)
# Extract centers
center_df <- data.frame(cluster, centers_2)

# Reshape the data
center_reshape <- gather(center_df, features, values, PCS.1:PCS.22)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
# Generate plot
g_heat_1
```

```{r}
# Create vector of clusters
cluster <- c(1: 2)
# Extract centers
center_df <- data.frame(cluster, centers_2)

# Reshape the data
center_reshape <- gather(center_df, features, values, MFQ.1:MFQ.33)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
# Generate plot
g_heat_1
```

```{r}
#want our clusters to be balanced if possible (bad if cluster w much lower value)
plot_clust_cardinality <- as.data.frame(clusters_2)

names(plot_clust_cardinality) <- c("k_2") # Set names

# Create bar plots
g_2 <- ggplot(plot_clust_cardinality, aes( x = factor(k_2))) + # Set x as cluster values
  geom_bar(stat = "count", fill = "steelblue") + # Use geom_bar with stat = "count" to count observations
    labs(x = "Cluster Number", y="Points in Cluster", # Set labels
         title = "Cluster Cardinality (k = 4)") +
  theme(panel.grid.major = element_blank(), # Turn of the background grid
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank()) 
g_2
```


```{r}
#plotting cluster magnitude
#sum of distances of points to the center cluster
k_4_mag <- cbind.data.frame(c(1:2), fit_2$withinss) # Extract within cluster sum of squares

names(k_4_mag) <- c("cluster", "withinss") # Fix names for plot data


# Create bar plot
g_4 <- ggplot(k_4_mag, aes(x = cluster, y = withinss)) + # Set x as cluster, y as withinss
  geom_bar(stat = "identity", fill = "steelblue") + # Use geom bar and stat = "identity" to plot values directly
   labs(x = "Cluster Number", y="Total Point to Centroid Distance", # Set labels
         title = "Cluster Magnitude (k = 2)") +
  theme(panel.grid.major = element_blank(), # Turn of the background grid
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank()) 

g_4
```

```{r}
k_4_dat <- cbind.data.frame(table(clusters_2), k_4_mag[,2]) # Join magnitude and cardinality

names(k_4_dat) <- c("cluster", "cardinality", "magnitude") # Fix plot data names # card = how many samples there are and magnitude = how much error there is in each cluster

# Create scatter plot
g_6 <- ggplot(k_4_dat, aes(x = cardinality, y = magnitude, color = cluster)) + # Set aesthetics
  geom_point(alpha = 0.8, size  = 4) +  # Set geom point for scatter
 geom_smooth(aes(x = cardinality, y = magnitude), method = "lm",
              se = FALSE, inherit.aes = FALSE, alpha = 0.5) + # Set trend  line
  labs(x = "Cluster Cardinality", y="Total Point to Centroid Distance", # Set labels
         title = "Cluster Magnitude vs Cardinality \n(k = 2)") +
  theme(panel.grid.major = element_blank(), # Turn of the background grid
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank()) 

g_6
```

```{r}
# Calculate distance between samples
dis = dist(sdata2)^2
# Set plotting parameters to view plot
op <- par(mfrow= c(1,1), oma= c(0,0, 3, 0),
          mgp= c(1.6,.8,0), mar= .1+c(4,2,2,2))
# Create silhouette for k=4
#how similar sample is to others in its cluster/how dissimilar it is to vals in otherclusters
#want values to be as high as possible, if negative val more similar to vals in other clusters
sil = silhouette (clusters_2 , # Set clustering
                  dis, # Set distance 
                  full = TRUE) # Generate silhouette for all samples
# Generate silhouette plot
plot(sil)
```

```{r}
# Create silhouette plot summary
fviz_nbclust(sdata2[clusters_2 ==1,], # Set dataset
             kmeans,# Set clustering method
             method = "silhouette") # Set evaluation method
```

Smaller group of data from sillouhette plot

```{r}

set.seed(12345) # Set seed for reproducibility
fit_3 <- kmeans(x = sdata2[clusters_2 == 1,], # Set data as explantory variables 
                centers = 2,  # Set number of clusters
                nstart = 25, # Set number of starts
                iter.max = 100 ) # Set maximum number of iterations to use
```


```{r}
# Extract clusters
clusters_3 <- fit_3$cluster
# Extract centers
centers_3 <- fit_3$centers
# Checksamples per cluster
summary(as.factor(clusters_3))
```

```{r}
sdata3 <- sdata2[clusters_2 ==1,][clusters_3 != 2,]
# Create silhouette plot summary
fviz_nbclust(sdata3, # Set dataset
             kmeans,# Set clustering method
             method = "silhouette") # Set evaluation method
```


```{r}

set.seed(12345) # Set seed for reproducibility
fit_4 <- kmeans(x = sdata3, # Set data as explantory variables 
                centers = 3,  # Set number of clusters
                nstart = 25, # Set number of starts
                iter.max = 100 ) # Set maximum number of iterations to use
```


```{r}
# Extract clusters
clusters_4 <- fit_4$cluster
# Extract centers
centers_4 <- fit_4$centers
# Checksamples per cluster
summary(as.factor(clusters_4))
```

Bigger group of data from silhouette plot

```{r}
sdata5 <- sdata2[clusters_2 ==2,]
# Create silhouette plot summary
fviz_nbclust(sdata5, # Set dataset
             kmeans,# Set clustering method
             method = "silhouette") # Set evaluation method
```

```{r}
set.seed(12345) # Set seed for reproducibility
fit_5 <- kmeans(x = sdata2[clusters_2 == 2,], # Set data as explantory variables 
                centers = 4,  # Set number of clusters
                nstart = 25, # Set number of starts
                iter.max = 100 ) # Set maximum number of iterations to use
```

```{r}
# Extract clusters
clusters_5 <- fit_5$cluster
# Extract centers
centers_5 <- fit_5$centers
# Checksamples per cluster
summary(as.factor(clusters_5))
```

```{r}
# Create vector of clusters
cluster <- c(1: 4)
# Extract centers
center_df <- data.frame(cluster, centers_5)

# Reshape the data
center_reshape <- gather(center_df, features, values, Age..Years.:MFQ.Cut.off)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
# Generate plot
g_heat_1
```

```{r}
# Create vector of clusters
cluster <- c(1: 4)
# Extract centers
center_df <- data.frame(cluster, centers_5)

# Reshape the data
center_reshape <- gather(center_df, features, values, PCS.1:PCS.22)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
# Generate plot
g_heat_1
```

```{r}
# Create vector of clusters
cluster <- c(1: 4)
# Extract centers
center_df <- data.frame(cluster, centers_5)

# Reshape the data
center_reshape <- gather(center_df, features, values, MFQ.1:MFQ.33)
# View first few rows
head(center_reshape)

# Create plot
g_heat_1 <- ggplot(data = center_reshape, # Set dataset
                   aes(x = features, y = cluster, fill = values)) + # Set aesthetics
  scale_y_continuous(breaks = seq(1, 5, by = 1)) + # Set y axis breaks
  geom_tile() + # Geom tile for heatmap
  coord_equal() +  # Make scale the same for both axis
  theme_set(theme_bw(base_size = 22) ) + # Set theme
  scale_fill_gradient2(low = "blue", # Choose low color
                       mid = "white", # Choose mid color
                       high = "red", # Choose high color
                       midpoint =0, # Choose mid point
                       space = "Lab", 
                       na.value ="grey", # Choose NA value
                       guide = "colourbar", # Set color bar
                       aesthetics = "fill") + # Select aesthetics to apply
  coord_flip() # Rotate plot to view names clearly
# Generate plot
g_heat_1
```

```{r}
plot_clust_cardinality <- as.data.frame(clusters_5)

names(plot_clust_cardinality) <- c("k_4") # Set names

# Create bar plots
g_6 <- ggplot(plot_clust_cardinality, aes( x = factor(k_4))) + # Set x as cluster values
  geom_bar(stat = "count", fill = "steelblue") + # Use geom_bar with stat = "count" to count observations
    labs(x = "Cluster Number", y="Points in Cluster", # Set labels
         title = "Cluster Cardinality (k = 4)") +
  theme(panel.grid.major = element_blank(), # Turn of the background grid
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank()) 
g_6
```

```{r}
k_5_mag <- cbind.data.frame(c(1:4), fit_5$withinss) # Extract within cluster sum of squares

names(k_5_mag) <- c("cluster", "withinss") # Fix names for plot data


# Create bar plot
g_7 <- ggplot(k_5_mag, aes(x = cluster, y = withinss)) + # Set x as cluster, y as withinss
  geom_bar(stat = "identity", fill = "steelblue") + # Use geom bar and stat = "identity" to plot values directly
   labs(x = "Cluster Number", y="Total Point to Centroid Distance", # Set labels
         title = "Cluster Magnitude (k = 4)") +
  theme(panel.grid.major = element_blank(), # Turn of the background grid
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank()) 

g_7
```

```{r}
k_5_dat <- cbind.data.frame(table(clusters_5), k_5_mag[,2]) # Join magnitude and cardinality

names(k_5_dat) <- c("cluster", "cardinality", "magnitude") # Fix plot data names # card = how many samples there are and magnitude = how much error there is in each cluster

# Create scatter plot
g_8 <- ggplot(k_5_dat, aes(x = cardinality, y = magnitude, color = cluster)) + # Set aesthetics
  geom_point(alpha = 0.8, size  = 4) +  # Set geom point for scatter
 geom_smooth(aes(x = cardinality, y = magnitude), method = "lm",
              se = FALSE, inherit.aes = FALSE, alpha = 0.5) + # Set trend  line
  labs(x = "Cluster Cardinality", y="Total Point to Centroid Distance", # Set labels
         title = "Cluster Magnitude vs Cardinality \n(k = 4)") +
  theme(panel.grid.major = element_blank(), # Turn of the background grid
        panel.grid.minor = element_blank(),
        panel.border = element_blank(),
        panel.background = element_blank()) 

g_8
```
```{r}

```

